[
  {
    "name": "Canonical driver",
    "description": "Synthetic canonical driver sweep; only declared fields change while the topic contract remains fixed.",
    "canonical_step": 30,
    "summary": {
      "focus_step": 30,
      "focus_kind": "canonical-fixture",
      "canonical_output_match": true,
      "state_counts": {
        "calculated": 61
      },
      "value_min": 1.967472977696,
      "value_max": 13.071088577292,
      "segments": [
        {
          "start_step": 0,
          "end_step": 60,
          "state": "calculated",
          "decision": "bharath-shumway-naive-approximation",
          "start_value_label": "13.0711 sigma",
          "end_value_label": "1.9675 sigma"
        }
      ]
    },
    "states": [
      {
        "step": 0,
        "value": 13.071088577292,
        "value_label": "13.0711 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 13.0711 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.08,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.07,
          "naive_asset_volatility": 0.076,
          "naive_distance_to_default": 13.071088577292,
          "naive_default_probability": 0.0,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 1,
        "value": 12.064448200172,
        "value_label": "12.0644 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 12.0644 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.089,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.07225,
          "naive_asset_volatility": 0.0823,
          "naive_distance_to_default": 12.064448200172,
          "naive_default_probability": 0.0,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 2,
        "value": 11.200516386841,
        "value_label": "11.2005 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 11.2005 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.098,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.0745,
          "naive_asset_volatility": 0.0886,
          "naive_distance_to_default": 11.200516386841,
          "naive_default_probability": 0.0,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 3,
        "value": 10.450871726809,
        "value_label": "10.4509 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 10.4509 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.107,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.07675,
          "naive_asset_volatility": 0.0949,
          "naive_distance_to_default": 10.450871726809,
          "naive_default_probability": 0.0,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 4,
        "value": 9.794170077808,
        "value_label": "9.7942 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 9.7942 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.116,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.079,
          "naive_asset_volatility": 0.1012,
          "naive_distance_to_default": 9.794170077808,
          "naive_default_probability": 0.0,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 5,
        "value": 9.21407076162,
        "value_label": "9.2141 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 9.2141 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.125,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.08125,
          "naive_asset_volatility": 0.1075,
          "naive_distance_to_default": 9.21407076162,
          "naive_default_probability": 0.0,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 6,
        "value": 8.697851598191,
        "value_label": "8.6979 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 8.6979 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.134,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.0835,
          "naive_asset_volatility": 0.1138,
          "naive_distance_to_default": 8.697851598191,
          "naive_default_probability": 0.0,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 7,
        "value": 8.235459840751,
        "value_label": "8.2355 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 8.2355 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.143,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.08575,
          "naive_asset_volatility": 0.1201,
          "naive_distance_to_default": 8.235459840751,
          "naive_default_probability": 0.0,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 8,
        "value": 7.818846929384,
        "value_label": "7.8188 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 7.8188 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.152,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.088,
          "naive_asset_volatility": 0.1264,
          "naive_distance_to_default": 7.818846929384,
          "naive_default_probability": 0.0,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 9,
        "value": 7.441492742081,
        "value_label": "7.4415 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 7.4415 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.161,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.09025,
          "naive_asset_volatility": 0.1327,
          "naive_distance_to_default": 7.441492742081,
          "naive_default_probability": 0.0,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 10,
        "value": 7.098059222116,
        "value_label": "7.0981 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 7.0981 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.17,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.0925,
          "naive_asset_volatility": 0.139,
          "naive_distance_to_default": 7.098059222116,
          "naive_default_probability": 1e-12,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 11,
        "value": 6.784134114757,
        "value_label": "6.7841 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 6.7841 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.179,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.09475,
          "naive_asset_volatility": 0.1453,
          "naive_distance_to_default": 6.784134114757,
          "naive_default_probability": 6e-12,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 12,
        "value": 6.496038600753,
        "value_label": "6.4960 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 6.4960 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.188,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.097,
          "naive_asset_volatility": 0.1516,
          "naive_distance_to_default": 6.496038600753,
          "naive_default_probability": 4.1e-11,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 13,
        "value": 6.230680980837,
        "value_label": "6.2307 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 6.2307 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.197,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.09925,
          "naive_asset_volatility": 0.1579,
          "naive_distance_to_default": 6.230680980837,
          "naive_default_probability": 2.32e-10,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 14,
        "value": 5.985444043083,
        "value_label": "5.9854 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.9854 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.206,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1015,
          "naive_asset_volatility": 0.1642,
          "naive_distance_to_default": 5.985444043083,
          "naive_default_probability": 1.079e-09,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 15,
        "value": 5.758097401021,
        "value_label": "5.7581 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.7581 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.215,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.10375,
          "naive_asset_volatility": 0.1705,
          "naive_distance_to_default": 5.758097401021,
          "naive_default_probability": 4.253e-09,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 16,
        "value": 5.546728573949,
        "value_label": "5.5467 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.5467 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.224,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.106,
          "naive_asset_volatility": 0.1768,
          "naive_distance_to_default": 5.546728573949,
          "naive_default_probability": 1.4553e-08,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 17,
        "value": 5.349688295326,
        "value_label": "5.3497 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.3497 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.233,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.10825,
          "naive_asset_volatility": 0.1831,
          "naive_distance_to_default": 5.349688295326,
          "naive_default_probability": 4.4053e-08,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 18,
        "value": 5.1655467364,
        "value_label": "5.1655 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.1655 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.242,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1105,
          "naive_asset_volatility": 0.1894,
          "naive_distance_to_default": 5.1655467364,
          "naive_default_probability": 1.19869e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 19,
        "value": 4.993058185356,
        "value_label": "4.9931 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.9931 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.251,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.11275,
          "naive_asset_volatility": 0.1957,
          "naive_distance_to_default": 4.993058185356,
          "naive_default_probability": 2.97153e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 20,
        "value": 4.831132336011,
        "value_label": "4.8311 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.8311 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.26,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.115,
          "naive_asset_volatility": 0.202,
          "naive_distance_to_default": 4.831132336011,
          "naive_default_probability": 6.78794e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 21,
        "value": 4.678810786722,
        "value_label": "4.6788 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.6788 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.269,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.11725,
          "naive_asset_volatility": 0.2083,
          "naive_distance_to_default": 4.678810786722,
          "naive_default_probability": 1.442718e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 22,
        "value": 4.535247678817,
        "value_label": "4.5352 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.5352 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.278,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1195,
          "naive_asset_volatility": 0.2146,
          "naive_distance_to_default": 4.535247678817,
          "naive_default_probability": 2.876796e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 23,
        "value": 4.39969364814,
        "value_label": "4.3997 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.3997 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.287,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.12175,
          "naive_asset_volatility": 0.2209,
          "naive_distance_to_default": 4.39969364814,
          "naive_default_probability": 5.42019e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 24,
        "value": 4.271482446629,
        "value_label": "4.2715 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.2715 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.296,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.124,
          "naive_asset_volatility": 0.2272,
          "naive_distance_to_default": 4.271482446629,
          "naive_default_probability": 9.708891e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 25,
        "value": 4.150019729654,
        "value_label": "4.1500 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.1500 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.305,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.12625,
          "naive_asset_volatility": 0.2335,
          "naive_distance_to_default": 4.150019729654,
          "naive_default_probability": 1.6622331e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 26,
        "value": 4.034773610818,
        "value_label": "4.0348 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.0348 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.314,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1285,
          "naive_asset_volatility": 0.2398,
          "naive_distance_to_default": 4.034773610818,
          "naive_default_probability": 2.7327484e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 27,
        "value": 3.92526666751,
        "value_label": "3.9253 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.9253 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.323,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.13075,
          "naive_asset_volatility": 0.2461,
          "naive_distance_to_default": 3.92526666751,
          "naive_default_probability": 4.3316855e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 28,
        "value": 3.821069143717,
        "value_label": "3.8211 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.8211 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.332,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.133,
          "naive_asset_volatility": 0.2524,
          "naive_distance_to_default": 3.821069143717,
          "naive_default_probability": 6.6437195e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 29,
        "value": 3.721793146015,
        "value_label": "3.7218 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.7218 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.341,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.13525,
          "naive_asset_volatility": 0.2587,
          "naive_distance_to_default": 3.721793146015,
          "naive_default_probability": 9.8906522e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 30,
        "value": 3.62708766745,
        "value_label": "3.6271 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.6271 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.62708766745,
          "naive_default_probability": 0.000143317997,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 31,
        "value": 3.536634304733,
        "value_label": "3.5366 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.5366 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.359,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.13975,
          "naive_asset_volatility": 0.2713,
          "naive_distance_to_default": 3.536634304733,
          "naive_default_probability": 0.000202630194,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 32,
        "value": 3.450143558624,
        "value_label": "3.4501 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.4501 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.368,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.142,
          "naive_asset_volatility": 0.2776,
          "naive_distance_to_default": 3.450143558624,
          "naive_default_probability": 0.000280144259,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 33,
        "value": 3.36735162689,
        "value_label": "3.3674 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.3674 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.377,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.14425,
          "naive_asset_volatility": 0.2839,
          "naive_distance_to_default": 3.36735162689,
          "naive_default_probability": 0.000379469265,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 34,
        "value": 3.288017615004,
        "value_label": "3.2880 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.2880 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.386,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1465,
          "naive_asset_volatility": 0.2902,
          "naive_distance_to_default": 3.288017615004,
          "naive_default_probability": 0.000504477632,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 35,
        "value": 3.211921102442,
        "value_label": "3.2119 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.2119 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.395,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.14875,
          "naive_asset_volatility": 0.2965,
          "naive_distance_to_default": 3.211921102442,
          "naive_default_probability": 0.000659252899,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 36,
        "value": 3.138860012794,
        "value_label": "3.1389 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.1389 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.404,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.151,
          "naive_asset_volatility": 0.3028,
          "naive_distance_to_default": 3.138860012794,
          "naive_default_probability": 0.000848032255,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 37,
        "value": 3.068648744336,
        "value_label": "3.0686 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.0686 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.413,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.15325,
          "naive_asset_volatility": 0.3091,
          "naive_distance_to_default": 3.068648744336,
          "naive_default_probability": 0.001075146265,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 38,
        "value": 3.001116524649,
        "value_label": "3.0011 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.0011 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.422,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1555,
          "naive_asset_volatility": 0.3154,
          "naive_distance_to_default": 3.001116524649,
          "naive_default_probability": 0.001344958043,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 39,
        "value": 2.936105958577,
        "value_label": "2.9361 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.9361 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.431,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.15775,
          "naive_asset_volatility": 0.3217,
          "naive_distance_to_default": 2.936105958577,
          "naive_default_probability": 0.001661803874,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 40,
        "value": 2.873471743519,
        "value_label": "2.8735 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.8735 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.44,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.16,
          "naive_asset_volatility": 0.328,
          "naive_distance_to_default": 2.873471743519,
          "naive_default_probability": 0.002029936967,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 41,
        "value": 2.813079529986,
        "value_label": "2.8131 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.8131 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.449,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.16225,
          "naive_asset_volatility": 0.3343,
          "naive_distance_to_default": 2.813079529986,
          "naive_default_probability": 0.002453475664,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 42,
        "value": 2.754804908615,
        "value_label": "2.7548 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7548 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.458,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1645,
          "naive_asset_volatility": 0.3406,
          "naive_distance_to_default": 2.754804908615,
          "naive_default_probability": 0.002936357071,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 43,
        "value": 2.698532507565,
        "value_label": "2.6985 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.6985 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.467,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.16675,
          "naive_asset_volatility": 0.3469,
          "naive_distance_to_default": 2.698532507565,
          "naive_default_probability": 0.003482296777,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 44,
        "value": 2.644155186507,
        "value_label": "2.6442 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.6442 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.476,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.169,
          "naive_asset_volatility": 0.3532,
          "naive_distance_to_default": 2.644155186507,
          "naive_default_probability": 0.00409475498,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 45,
        "value": 2.591573315366,
        "value_label": "2.5916 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5916 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.485,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.17125,
          "naive_asset_volatility": 0.3595,
          "naive_distance_to_default": 2.591573315366,
          "naive_default_probability": 0.00477690912,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 46,
        "value": 2.540694127595,
        "value_label": "2.5407 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5407 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.494,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1735,
          "naive_asset_volatility": 0.3658,
          "naive_distance_to_default": 2.540694127595,
          "naive_default_probability": 0.005531632894,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 47,
        "value": 2.49143113914,
        "value_label": "2.4914 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4914 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.503,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.17575,
          "naive_asset_volatility": 0.3721,
          "naive_distance_to_default": 2.49143113914,
          "naive_default_probability": 0.006361481353,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 48,
        "value": 2.44370362546,
        "value_label": "2.4437 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4437 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.512,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.178,
          "naive_asset_volatility": 0.3784,
          "naive_distance_to_default": 2.44370362546,
          "naive_default_probability": 0.007268681674,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 49,
        "value": 2.39743614992,
        "value_label": "2.3974 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.3974 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.521,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.18025,
          "naive_asset_volatility": 0.3847,
          "naive_distance_to_default": 2.39743614992,
          "naive_default_probability": 0.00825512909,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 50,
        "value": 2.352558137786,
        "value_label": "2.3526 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.3526 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.53,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1825,
          "naive_asset_volatility": 0.391,
          "naive_distance_to_default": 2.352558137786,
          "naive_default_probability": 0.009322387446,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 51,
        "value": 2.309003490748,
        "value_label": "2.3090 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.3090 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.539,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.18475,
          "naive_asset_volatility": 0.3973,
          "naive_distance_to_default": 2.309003490748,
          "naive_default_probability": 0.010471693769,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 52,
        "value": 2.266710237547,
        "value_label": "2.2667 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.2667 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.548,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.187,
          "naive_asset_volatility": 0.4036,
          "naive_distance_to_default": 2.266710237547,
          "naive_default_probability": 0.011703966306,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 53,
        "value": 2.225620216819,
        "value_label": "2.2256 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.2256 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.557,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.18925,
          "naive_asset_volatility": 0.4099,
          "naive_distance_to_default": 2.225620216819,
          "naive_default_probability": 0.013019815431,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 54,
        "value": 2.185678788741,
        "value_label": "2.1857 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.1857 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.566,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1915,
          "naive_asset_volatility": 0.4162,
          "naive_distance_to_default": 2.185678788741,
          "naive_default_probability": 0.014419556899,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 55,
        "value": 2.146834572483,
        "value_label": "2.1468 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.1468 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.575,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.19375,
          "naive_asset_volatility": 0.4225,
          "naive_distance_to_default": 2.146834572483,
          "naive_default_probability": 0.015903226949,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 56,
        "value": 2.109039206796,
        "value_label": "2.1090 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.1090 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.584,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.196,
          "naive_asset_volatility": 0.4288,
          "naive_distance_to_default": 2.109039206796,
          "naive_default_probability": 0.017470598785,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 57,
        "value": 2.072247131405,
        "value_label": "2.0722 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.0722 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.593,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.19825,
          "naive_asset_volatility": 0.4351,
          "naive_distance_to_default": 2.072247131405,
          "naive_default_probability": 0.019121200033,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 58,
        "value": 2.036415387119,
        "value_label": "2.0364 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.0364 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.602,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.2005,
          "naive_asset_volatility": 0.4414,
          "naive_distance_to_default": 2.036415387119,
          "naive_default_probability": 0.020854330813,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 59,
        "value": 2.001503432821,
        "value_label": "2.0015 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.0015 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.611,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.20275,
          "naive_asset_volatility": 0.4477,
          "naive_distance_to_default": 2.001503432821,
          "naive_default_probability": 0.022669082102,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 60,
        "value": 1.967472977696,
        "value_label": "1.9675 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.9675 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.62,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.205,
          "naive_asset_volatility": 0.454,
          "naive_distance_to_default": 1.967472977696,
          "naive_default_probability": 0.024564354121,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      }
    ]
  },
  {
    "name": "Adverse shift",
    "description": "Synthetic adverse shift sweep; only declared fields change while the topic contract remains fixed.",
    "canonical_step": 30,
    "summary": {
      "focus_step": 30,
      "focus_kind": "comparison",
      "canonical_output_match": false,
      "state_counts": {
        "calculated": 61
      },
      "value_min": 2.423797060916,
      "value_max": 5.340357032306,
      "segments": [
        {
          "start_step": 0,
          "end_step": 60,
          "state": "calculated",
          "decision": "bharath-shumway-naive-approximation",
          "start_value_label": "5.3404 sigma",
          "end_value_label": "2.4238 sigma"
        }
      ]
    },
    "states": [
      {
        "step": 0,
        "value": 5.340357032306,
        "value_label": "5.3404 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.3404 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 30.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 150.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.3075,
          "naive_distance_to_default": 5.340357032306,
          "naive_default_probability": 4.6382e-08,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 1,
        "value": 5.163784881611,
        "value_label": "5.1638 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.1638 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 32.833333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 152.833333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.304348418757,
          "naive_distance_to_default": 5.163784881611,
          "naive_default_probability": 1.21003e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 2,
        "value": 5.005138462976,
        "value_label": "5.0051 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.0051 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 35.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 155.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.301311563169,
          "naive_distance_to_default": 5.005138462976,
          "naive_default_probability": 2.79109e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 3,
        "value": 4.86146561974,
        "value_label": "4.8615 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.8615 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 38.5,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 158.5,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.298383280757,
          "naive_distance_to_default": 4.86146561974,
          "naive_default_probability": 5.82599e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 4,
        "value": 4.730465164545,
        "value_label": "4.7305 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.7305 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 41.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 161.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.29555785124,
          "naive_distance_to_default": 4.730465164545,
          "naive_default_probability": 1.12003e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 5,
        "value": 4.61031096413,
        "value_label": "4.6103 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.6103 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 44.166666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 164.166666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.292829949239,
          "naive_distance_to_default": 4.61031096413,
          "naive_default_probability": 2.010335e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 6,
        "value": 4.499531370144,
        "value_label": "4.4995 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.4995 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 47.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 167.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.290194610778,
          "naive_distance_to_default": 4.499531370144,
          "naive_default_probability": 3.405171e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 7,
        "value": 4.396924389624,
        "value_label": "4.3969 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.3969 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 49.833333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 169.833333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.28764720314,
          "naive_distance_to_default": 4.396924389624,
          "naive_default_probability": 5.489779e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 8,
        "value": 4.301496630029,
        "value_label": "4.3015 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.3015 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 52.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 172.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.285183397683,
          "naive_distance_to_default": 4.301496630029,
          "naive_default_probability": 8.482418e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 9,
        "value": 4.212418473197,
        "value_label": "4.2124 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.2124 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 55.5,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 175.5,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.282799145299,
          "naive_distance_to_default": 4.212418473197,
          "naive_default_probability": 1.2632546e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 10,
        "value": 4.128990581537,
        "value_label": "4.1290 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.1290 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 58.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 178.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.280490654206,
          "naive_distance_to_default": 4.128990581537,
          "naive_default_probability": 1.8217966e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 11,
        "value": 4.050618477659,
        "value_label": "4.0506 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.0506 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 61.166666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 181.166666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.278254369825,
          "naive_distance_to_default": 4.050618477659,
          "naive_default_probability": 2.5541219e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 12,
        "value": 3.97679297965,
        "value_label": "3.9768 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.9768 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 64.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 184.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.276086956522,
          "naive_distance_to_default": 3.97679297965,
          "naive_default_probability": 3.4925462e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 13,
        "value": 3.907074952202,
        "value_label": "3.9071 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.9071 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 66.833333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 186.833333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.273985280999,
          "naive_distance_to_default": 3.907074952202,
          "naive_default_probability": 4.6710091e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 14,
        "value": 3.841083285128,
        "value_label": "3.8411 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.8411 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 69.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 189.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.271946397188,
          "naive_distance_to_default": 3.841083285128,
          "naive_default_probability": 6.1246271e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 15,
        "value": 3.778485317291,
        "value_label": "3.7785 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.7785 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 72.5,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 192.5,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.269967532468,
          "naive_distance_to_default": 3.778485317291,
          "naive_default_probability": 7.8892577e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 16,
        "value": 3.718989135741,
        "value_label": "3.7190 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.7190 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 75.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 195.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.268046075085,
          "naive_distance_to_default": 3.718989135741,
          "naive_default_probability": 0.000100010827,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 17,
        "value": 3.662337328692,
        "value_label": "3.6623 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.6623 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 78.166666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 198.166666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.266179562658,
          "naive_distance_to_default": 3.662337328692,
          "naive_default_probability": 0.000124962228,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 18,
        "value": 3.60830187706,
        "value_label": "3.6083 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.6083 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 81.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 201.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.264365671642,
          "naive_distance_to_default": 3.60830187706,
          "naive_default_probability": 0.000154103873,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 19,
        "value": 3.556679945979,
        "value_label": "3.5567 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.5567 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 83.833333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 203.833333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.262602207686,
          "naive_distance_to_default": 3.556679945979,
          "naive_default_probability": 0.000187785627,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 20,
        "value": 3.507290393836,
        "value_label": "3.5073 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.5073 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 86.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 206.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.260887096774,
          "naive_distance_to_default": 3.507290393836,
          "naive_default_probability": 0.000226347418,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 21,
        "value": 3.459970857952,
        "value_label": "3.4600 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.4600 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 89.5,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 209.5,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.259218377088,
          "naive_distance_to_default": 3.459970857952,
          "naive_default_probability": 0.000270116926,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 22,
        "value": 3.414575307122,
        "value_label": "3.4146 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.4146 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 92.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 212.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.257594191523,
          "naive_distance_to_default": 3.414575307122,
          "naive_default_probability": 0.000319407657,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 23,
        "value": 3.370971974771,
        "value_label": "3.3710 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.3710 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 95.166666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 215.166666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.25601278079,
          "naive_distance_to_default": 3.370971974771,
          "naive_default_probability": 0.000374517387,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 24,
        "value": 3.329041604421,
        "value_label": "3.3290 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.3290 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 98.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 218.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.254472477064,
          "naive_distance_to_default": 3.329041604421,
          "naive_default_probability": 0.000435726928,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 25,
        "value": 3.288675952968,
        "value_label": "3.2887 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.2887 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 100.833333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 220.833333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.252971698113,
          "naive_distance_to_default": 3.288675952968,
          "naive_default_probability": 0.00050329922,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 26,
        "value": 3.249776508015,
        "value_label": "3.2498 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.2498 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 103.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 223.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.251508941878,
          "naive_distance_to_default": 3.249776508015,
          "naive_default_probability": 0.000577478683,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 27,
        "value": 3.212253383871,
        "value_label": "3.2123 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.2123 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 106.5,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 226.5,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.250082781457,
          "naive_distance_to_default": 3.212253383871,
          "naive_default_probability": 0.000658490823,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 28,
        "value": 3.176024367429,
        "value_label": "3.1760 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.1760 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 109.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 229.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.248691860465,
          "naive_distance_to_default": 3.176024367429,
          "naive_default_probability": 0.000746542045,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 29,
        "value": 3.141014090389,
        "value_label": "3.1410 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.1410 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 112.166666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 232.166666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.247334888729,
          "naive_distance_to_default": 3.141014090389,
          "naive_default_probability": 0.00084181966,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 30,
        "value": 3.107153308458,
        "value_label": "3.1072 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.1072 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 115.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 235.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.246010638298,
          "naive_distance_to_default": 3.107153308458,
          "naive_default_probability": 0.000944492042,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 31,
        "value": 3.074378271512,
        "value_label": "3.0744 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.0744 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 117.833333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 237.833333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.244717939734,
          "naive_distance_to_default": 3.074378271512,
          "naive_default_probability": 0.001054708924,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 32,
        "value": 3.042630171431,
        "value_label": "3.0426 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.0426 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 120.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 240.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.24345567867,
          "naive_distance_to_default": 3.042630171431,
          "naive_default_probability": 0.001172601804,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 33,
        "value": 3.011854656496,
        "value_label": "3.0119 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.0119 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 123.5,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 243.5,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.242222792608,
          "naive_distance_to_default": 3.011854656496,
          "naive_default_probability": 0.001298284443,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 34,
        "value": 2.982001403054,
        "value_label": "2.9820 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.9820 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 126.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 246.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.24101826793,
          "naive_distance_to_default": 2.982001403054,
          "naive_default_probability": 0.001431853432,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 35,
        "value": 2.953023736614,
        "value_label": "2.9530 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.9530 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 129.166666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 249.166666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.239841137124,
          "naive_distance_to_default": 2.953023736614,
          "naive_default_probability": 0.001573388827,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 36,
        "value": 2.924878295755,
        "value_label": "2.9249 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.9249 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 132.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 252.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.23869047619,
          "naive_distance_to_default": 2.924878295755,
          "naive_default_probability": 0.00172295481,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 37,
        "value": 2.897524733234,
        "value_label": "2.8975 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.8975 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 134.833333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 254.833333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.237565402224,
          "naive_distance_to_default": 2.897524733234,
          "naive_default_probability": 0.0018806004,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 38,
        "value": 2.870925449512,
        "value_label": "2.8709 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.8709 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 137.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 257.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.236465071151,
          "naive_distance_to_default": 2.870925449512,
          "naive_default_probability": 0.002046360173,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 39,
        "value": 2.84504535462,
        "value_label": "2.8450 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.8450 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 140.5,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 260.5,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.235388675624,
          "naive_distance_to_default": 2.84504535462,
          "naive_default_probability": 0.002220254992,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 40,
        "value": 2.819851654854,
        "value_label": "2.8199 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.8199 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 143.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 263.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.234335443038,
          "naive_distance_to_default": 2.819851654854,
          "naive_default_probability": 0.002402292754,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 41,
        "value": 2.795313661298,
        "value_label": "2.7953 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7953 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 146.166666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 266.166666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.233304633688,
          "naive_distance_to_default": 2.795313661298,
          "naive_default_probability": 0.002592469121,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 42,
        "value": 2.771402617578,
        "value_label": "2.7714 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7714 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 149.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 269.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.232295539033,
          "naive_distance_to_default": 2.771402617578,
          "naive_default_probability": 0.002790768248,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 43,
        "value": 2.748091544596,
        "value_label": "2.7481 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7481 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 151.833333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 271.833333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.231307480074,
          "naive_distance_to_default": 2.748091544596,
          "naive_default_probability": 0.002997163504,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 44,
        "value": 2.725355100306,
        "value_label": "2.7254 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7254 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 154.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 274.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.230339805825,
          "naive_distance_to_default": 2.725355100306,
          "naive_default_probability": 0.003211618168,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 45,
        "value": 2.703169452825,
        "value_label": "2.7032 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7032 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 157.5,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 277.5,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.229391891892,
          "naive_distance_to_default": 2.703169452825,
          "naive_default_probability": 0.003434086116,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 46,
        "value": 2.681512165413,
        "value_label": "2.6815 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.6815 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 160.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 280.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.22846313912,
          "naive_distance_to_default": 2.681512165413,
          "naive_default_probability": 0.003664512479,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 47,
        "value": 2.660362092024,
        "value_label": "2.6604 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.6604 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 163.166666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 283.166666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.227552972337,
          "naive_distance_to_default": 2.660362092024,
          "naive_default_probability": 0.003902834281,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 48,
        "value": 2.639699282302,
        "value_label": "2.6397 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.6397 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 166.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 286.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.226660839161,
          "naive_distance_to_default": 2.639699282302,
          "naive_default_probability": 0.004148981058,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 49,
        "value": 2.619504895018,
        "value_label": "2.6195 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.6195 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 168.833333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 288.833333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.225786208886,
          "naive_distance_to_default": 2.619504895018,
          "naive_default_probability": 0.004402875445,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 50,
        "value": 2.599761119085,
        "value_label": "2.5998 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5998 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 171.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 291.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.224928571429,
          "naive_distance_to_default": 2.599761119085,
          "naive_default_probability": 0.004664433744,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 51,
        "value": 2.58045110137,
        "value_label": "2.5805 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5805 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 174.5,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 294.5,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.224087436333,
          "naive_distance_to_default": 2.58045110137,
          "naive_default_probability": 0.004933566457,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 52,
        "value": 2.561558880622,
        "value_label": "2.5616 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5616 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 177.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 297.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.223262331839,
          "naive_distance_to_default": 2.561558880622,
          "naive_default_probability": 0.00521017881,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 53,
        "value": 2.543069326917,
        "value_label": "2.5431 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5431 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 180.166666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 300.166666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.222452803998,
          "naive_distance_to_default": 2.543069326917,
          "naive_default_probability": 0.005494171233,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 54,
        "value": 2.524968086081,
        "value_label": "2.5250 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5250 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 183.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 303.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.221658415842,
          "naive_distance_to_default": 2.524968086081,
          "naive_default_probability": 0.005785439826,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 55,
        "value": 2.507241528602,
        "value_label": "2.5072 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5072 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 185.833333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 305.833333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.220878746594,
          "naive_distance_to_default": 2.507241528602,
          "naive_default_probability": 0.006083876803,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 56,
        "value": 2.489876702628,
        "value_label": "2.4899 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4899 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 188.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 308.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.220113390929,
          "naive_distance_to_default": 2.489876702628,
          "naive_default_probability": 0.006389370899,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 57,
        "value": 2.472861290656,
        "value_label": "2.4729 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4729 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 191.5,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 311.5,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.219361958266,
          "naive_distance_to_default": 2.472861290656,
          "naive_default_probability": 0.006701807767,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 58,
        "value": 2.456183569571,
        "value_label": "2.4562 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4562 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 194.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 314.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.21862407211,
          "naive_distance_to_default": 2.456183569571,
          "naive_default_probability": 0.007021070349,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 59,
        "value": 2.439832373746,
        "value_label": "2.4398 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4398 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 197.166666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 317.166666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.217899369417,
          "naive_distance_to_default": 2.439832373746,
          "naive_default_probability": 0.007347039218,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 60,
        "value": 2.423797060916,
        "value_label": "2.4238 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4238 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 200.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 320.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.2171875,
          "naive_distance_to_default": 2.423797060916,
          "naive_default_probability": 0.007679592909,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      }
    ]
  },
  {
    "name": "Protective shift",
    "description": "Synthetic protective shift sweep; only declared fields change while the topic contract remains fixed.",
    "canonical_step": 30,
    "summary": {
      "focus_step": 30,
      "focus_kind": "comparison",
      "canonical_output_match": false,
      "state_counts": {
        "calculated": 61
      },
      "value_min": 1.940873212065,
      "value_max": 4.866308708038,
      "segments": [
        {
          "start_step": 0,
          "end_step": 60,
          "state": "calculated",
          "decision": "bharath-shumway-naive-approximation",
          "start_value_label": "1.9409 sigma",
          "end_value_label": "4.8663 sigma"
        }
      ]
    },
    "states": [
      {
        "step": 0,
        "value": 1.940873212065,
        "value_label": "1.9409 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.9409 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 30.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 110.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.195454545455,
          "naive_distance_to_default": 1.940873212065,
          "naive_default_probability": 0.026136828987,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 1,
        "value": 2.051265821549,
        "value_label": "2.0513 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.0513 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 33.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 113.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.200439882698,
          "naive_distance_to_default": 2.051265821549,
          "naive_default_probability": 0.020120533499,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 2,
        "value": 2.154690727444,
        "value_label": "2.1547 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.1547 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 37.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 117.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.205113636364,
          "naive_distance_to_default": 2.154690727444,
          "naive_default_probability": 0.015593021947,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 3,
        "value": 2.252069757224,
        "value_label": "2.2521 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.2521 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 41.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 121.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.209504132231,
          "naive_distance_to_default": 2.252069757224,
          "naive_default_probability": 0.012158932056,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 4,
        "value": 2.344154420223,
        "value_label": "2.3442 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.3442 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 44.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 124.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.213636363636,
          "naive_distance_to_default": 2.344154420223,
          "naive_default_probability": 0.009535136984,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 5,
        "value": 2.431564491179,
        "value_label": "2.4316 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4316 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 48.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 128.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.217532467532,
          "naive_distance_to_default": 2.431564491179,
          "naive_default_probability": 0.00751688584,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 6,
        "value": 2.514816473793,
        "value_label": "2.5148 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5148 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 52.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 132.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.221212121212,
          "naive_distance_to_default": 2.514816473793,
          "naive_default_probability": 0.005954718059,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 7,
        "value": 2.594344920499,
        "value_label": "2.5943 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5943 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 55.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 135.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.224692874693,
          "naive_distance_to_default": 2.594344920499,
          "naive_default_probability": 0.004738567855,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 8,
        "value": 2.670518623497,
        "value_label": "2.6705 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.6705 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 59.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 139.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.227990430622,
          "naive_distance_to_default": 2.670518623497,
          "naive_default_probability": 0.003786708511,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 9,
        "value": 2.743653066817,
        "value_label": "2.7437 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7437 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 63.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 143.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.231118881119,
          "naive_distance_to_default": 2.743653066817,
          "naive_default_probability": 0.003037985711,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 10,
        "value": 2.814020114104,
        "value_label": "2.8140 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.8140 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 66.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 146.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.234090909091,
          "naive_distance_to_default": 2.814020114104,
          "naive_default_probability": 0.002446308346,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 11,
        "value": 2.881855626305,
        "value_label": "2.8819 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.8819 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 70.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 150.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.236917960089,
          "naive_distance_to_default": 2.881855626305,
          "naive_default_probability": 0.00197670415,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 12,
        "value": 2.947365510667,
        "value_label": "2.9474 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.9474 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 74.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 154.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.23961038961,
          "naive_distance_to_default": 2.947365510667,
          "naive_default_probability": 0.001602470648,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 13,
        "value": 3.010730567937,
        "value_label": "3.0107 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.0107 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 77.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 157.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.242177589852,
          "naive_distance_to_default": 3.010730567937,
          "naive_default_probability": 0.001303099982,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 14,
        "value": 3.072110409478,
        "value_label": "3.0721 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.0721 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 81.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 161.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.244628099174,
          "naive_distance_to_default": 3.072110409478,
          "naive_default_probability": 0.001062755452,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 15,
        "value": 3.13164664777,
        "value_label": "3.1316 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.1316 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 85.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 165.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.24696969697,
          "naive_distance_to_default": 3.13164664777,
          "naive_default_probability": 0.000869144744,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 16,
        "value": 3.18946551424,
        "value_label": "3.1895 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.1895 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 88.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 168.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.249209486166,
          "naive_distance_to_default": 3.18946551424,
          "naive_default_probability": 0.000712680722,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 17,
        "value": 3.245680022049,
        "value_label": "3.2457 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.2457 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 92.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 172.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.251353965184,
          "naive_distance_to_default": 3.245680022049,
          "naive_default_probability": 0.00058585228,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 18,
        "value": 3.300391764503,
        "value_label": "3.3004 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.3004 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 96.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 176.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.253409090909,
          "naive_distance_to_default": 3.300391764503,
          "naive_default_probability": 0.000482749737,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 19,
        "value": 3.353692419574,
        "value_label": "3.3537 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.3537 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 99.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 179.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.255380333952,
          "naive_distance_to_default": 3.353692419574,
          "naive_default_probability": 0.000398704744,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 20,
        "value": 3.405665015773,
        "value_label": "3.4057 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.4057 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 103.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 183.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.257272727273,
          "naive_distance_to_default": 3.405665015773,
          "naive_default_probability": 0.000330015558,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 21,
        "value": 3.456385002994,
        "value_label": "3.4564 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.4564 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 107.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 187.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.259090909091,
          "naive_distance_to_default": 3.456385002994,
          "naive_default_probability": 0.000273736376,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 22,
        "value": 3.505921162996,
        "value_label": "3.5059 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.5059 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 110.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 190.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.260839160839,
          "naive_distance_to_default": 3.505921162996,
          "naive_default_probability": 0.000227514988,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 23,
        "value": 3.554336387291,
        "value_label": "3.5543 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.5543 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 114.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 194.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.262521440823,
          "naive_distance_to_default": 3.554336387291,
          "naive_default_probability": 0.000189467101,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 24,
        "value": 3.601688344786,
        "value_label": "3.6017 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.6017 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 118.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 198.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.264141414141,
          "naive_distance_to_default": 3.601688344786,
          "naive_default_probability": 0.000158078622,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 25,
        "value": 3.648030057293,
        "value_label": "3.6480 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.6480 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 121.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 201.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265702479339,
          "naive_distance_to_default": 3.648030057293,
          "naive_default_probability": 0.000132129364,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 26,
        "value": 3.693410397687,
        "value_label": "3.6934 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.6934 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 125.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 205.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.267207792208,
          "naive_distance_to_default": 3.693410397687,
          "naive_default_probability": 0.000110633248,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 27,
        "value": 3.737874522778,
        "value_label": "3.7379 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.7379 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 129.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 209.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.268660287081,
          "naive_distance_to_default": 3.737874522778,
          "naive_default_probability": 9.279126e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 28,
        "value": 3.781464250887,
        "value_label": "3.7815 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.7815 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 132.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 212.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.270062695925,
          "naive_distance_to_default": 3.781464250887,
          "naive_default_probability": 7.7954307e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 29,
        "value": 3.824218392347,
        "value_label": "3.8242 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.8242 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 136.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 216.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.271417565485,
          "naive_distance_to_default": 3.824218392347,
          "naive_default_probability": 6.5593797e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 30,
        "value": 3.866173039791,
        "value_label": "3.8662 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.8662 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 140.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 220.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.272727272727,
          "naive_distance_to_default": 3.866173039791,
          "naive_default_probability": 5.5278255e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 31,
        "value": 3.907361823952,
        "value_label": "3.9074 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.9074 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 143.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 223.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.273994038748,
          "naive_distance_to_default": 3.907361823952,
          "naive_default_probability": 4.6654685e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 32,
        "value": 3.947816139768,
        "value_label": "3.9478 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.9478 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 147.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 227.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.275219941349,
          "naive_distance_to_default": 3.947816139768,
          "naive_default_probability": 3.9433668e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 33,
        "value": 3.987565346834,
        "value_label": "3.9876 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.9876 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 151.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 231.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.276406926407,
          "naive_distance_to_default": 3.987565346834,
          "naive_default_probability": 3.337741e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 34,
        "value": 4.026636947626,
        "value_label": "4.0266 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.0266 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 154.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 234.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.277556818182,
          "naive_distance_to_default": 4.026636947626,
          "naive_default_probability": 2.8290146e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 35,
        "value": 4.065056746388,
        "value_label": "4.0651 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.0651 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 158.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 238.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.278671328671,
          "naive_distance_to_default": 4.065056746388,
          "naive_default_probability": 2.4010388e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 36,
        "value": 4.10284899115,
        "value_label": "4.1028 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.1028 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 162.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 242.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.279752066116,
          "naive_distance_to_default": 4.10284899115,
          "naive_default_probability": 2.0404681e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 37,
        "value": 4.140036500992,
        "value_label": "4.1400 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.1400 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 165.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 245.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.280800542741,
          "naive_distance_to_default": 4.140036500992,
          "naive_default_probability": 1.7362528e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 38,
        "value": 4.176640780367,
        "value_label": "4.1766 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.1766 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 169.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 249.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.281818181818,
          "naive_distance_to_default": 4.176640780367,
          "naive_default_probability": 1.4792284e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 39,
        "value": 4.21268212202,
        "value_label": "4.2127 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.2127 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 173.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 253.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.282806324111,
          "naive_distance_to_default": 4.21268212202,
          "naive_default_probability": 1.2617805e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 40,
        "value": 4.248179699865,
        "value_label": "4.2482 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.2482 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 176.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 256.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.283766233766,
          "naive_distance_to_default": 4.248179699865,
          "naive_default_probability": 1.0775725e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 41,
        "value": 4.283151652977,
        "value_label": "4.2832 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.2832 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 180.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 260.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.284699103713,
          "naive_distance_to_default": 4.283151652977,
          "naive_default_probability": 9.213224e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 42,
        "value": 4.317615161696,
        "value_label": "4.3176 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.3176 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 184.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 264.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.285606060606,
          "naive_distance_to_default": 4.317615161696,
          "naive_default_probability": 7.886206e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 43,
        "value": 4.351586516733,
        "value_label": "4.3516 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.3516 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 187.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 267.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.286488169365,
          "naive_distance_to_default": 4.351586516733,
          "naive_default_probability": 6.757798e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 44,
        "value": 4.385081182035,
        "value_label": "4.3851 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.3851 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 191.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 271.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.287346437346,
          "naive_distance_to_default": 4.385081182035,
          "naive_default_probability": 5.797127e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 45,
        "value": 4.418113852082,
        "value_label": "4.4181 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.4181 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 195.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 275.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.288181818182,
          "naive_distance_to_default": 4.418113852082,
          "naive_default_probability": 4.978299e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 46,
        "value": 4.450698504203,
        "value_label": "4.4507 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.4507 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 198.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 278.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.288995215311,
          "naive_distance_to_default": 4.450698504203,
          "naive_default_probability": 4.279572e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 47,
        "value": 4.482848446418,
        "value_label": "4.4828 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.4828 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 202.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 282.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.289787485242,
          "naive_distance_to_default": 4.482848446418,
          "naive_default_probability": 3.682662e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 48,
        "value": 4.514576361282,
        "value_label": "4.5146 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.5146 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 206.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 286.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.290559440559,
          "naive_distance_to_default": 4.514576361282,
          "naive_default_probability": 3.172173e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 49,
        "value": 4.545894346101,
        "value_label": "4.5459 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.5459 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 209.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 289.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.291311852704,
          "naive_distance_to_default": 4.545894346101,
          "naive_default_probability": 2.735124e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 50,
        "value": 4.576813949905,
        "value_label": "4.5768 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.5768 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 213.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 293.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.292045454545,
          "naive_distance_to_default": 4.576813949905,
          "naive_default_probability": 2.360555e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 51,
        "value": 4.607346207472,
        "value_label": "4.6073 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.6073 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 217.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 297.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.292760942761,
          "naive_distance_to_default": 4.607346207472,
          "naive_default_probability": 2.039203e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 52,
        "value": 4.637501670696,
        "value_label": "4.6375 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.6375 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 220.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 300.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.293458980044,
          "naive_distance_to_default": 4.637501670696,
          "naive_default_probability": 1.763229e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 53,
        "value": 4.667290437532,
        "value_label": "4.6673 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.6673 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 224.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 304.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.294140197152,
          "naive_distance_to_default": 4.667290437532,
          "naive_default_probability": 1.525989e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 54,
        "value": 4.696722178768,
        "value_label": "4.6967 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.6967 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 228.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 308.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.294805194805,
          "naive_distance_to_default": 4.696722178768,
          "naive_default_probability": 1.321848e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 55,
        "value": 4.725806162785,
        "value_label": "4.7258 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.7258 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 231.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 311.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.295454545455,
          "naive_distance_to_default": 4.725806162785,
          "naive_default_probability": 1.146021e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 56,
        "value": 4.754551278515,
        "value_label": "4.7546 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.7546 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 235.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 315.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.296088794926,
          "naive_distance_to_default": 4.754551278515,
          "naive_default_probability": 9.94438e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 57,
        "value": 4.782966056746,
        "value_label": "4.7830 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.7830 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 239.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 319.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.29670846395,
          "naive_distance_to_default": 4.782966056746,
          "naive_default_probability": 8.63637e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 58,
        "value": 4.8110586899,
        "value_label": "4.8111 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.8111 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 242.666666666667,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 322.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.297314049587,
          "naive_distance_to_default": 4.8110586899,
          "naive_default_probability": 7.50665e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 59,
        "value": 4.838837050447,
        "value_label": "4.8388 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.8388 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 246.333333333333,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 326.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.297906026558,
          "naive_distance_to_default": 4.838837050447,
          "naive_default_probability": 6.53005e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 60,
        "value": 4.866308708038,
        "value_label": "4.8663 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.8663 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 250.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 330.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.298484848485,
          "naive_distance_to_default": 4.866308708038,
          "naive_default_probability": 5.68509e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      }
    ]
  },
  {
    "name": "Threshold or boundary",
    "description": "Synthetic threshold or boundary sweep; only declared fields change while the topic contract remains fixed.",
    "canonical_step": 30,
    "summary": {
      "focus_step": 30,
      "focus_kind": "comparison",
      "canonical_output_match": false,
      "state_counts": {
        "calculated": 61
      },
      "value_min": 1.061049931601,
      "value_max": 5.589351818393,
      "segments": [
        {
          "start_step": 0,
          "end_step": 60,
          "state": "calculated",
          "decision": "bharath-shumway-naive-approximation",
          "start_value_label": "1.0610 sigma",
          "end_value_label": "5.5894 sigma"
        }
      ]
    },
    "states": [
      {
        "step": 0,
        "value": 1.061049931601,
        "value_label": "1.0610 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.0610 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.6,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 1.061049931601,
          "naive_default_probability": 0.144333605002,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 1,
        "value": 1.136521629714,
        "value_label": "1.1365 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.1365 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.58,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 1.136521629714,
          "naive_default_probability": 0.127869159213,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 2,
        "value": 1.211993327827,
        "value_label": "1.2120 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.2120 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.56,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 1.211993327827,
          "naive_default_probability": 0.11275746735,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 3,
        "value": 1.28746502594,
        "value_label": "1.2875 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.2875 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.54,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 1.28746502594,
          "naive_default_probability": 0.098966126107,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 4,
        "value": 1.362936724053,
        "value_label": "1.3629 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.3629 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.52,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 1.362936724053,
          "naive_default_probability": 0.086451226749,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 5,
        "value": 1.438408422167,
        "value_label": "1.4384 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.4384 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.5,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 1.438408422167,
          "naive_default_probability": 0.075159102183,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 6,
        "value": 1.51388012028,
        "value_label": "1.5139 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.5139 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.48,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 1.51388012028,
          "naive_default_probability": 0.065028123511,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 7,
        "value": 1.589351818393,
        "value_label": "1.5894 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.5894 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.46,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 1.589351818393,
          "naive_default_probability": 0.055990492965,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 8,
        "value": 1.664823516506,
        "value_label": "1.6648 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.6648 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.44,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 1.664823516506,
          "naive_default_probability": 0.047973985382,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 9,
        "value": 1.740295214619,
        "value_label": "1.7403 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.7403 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.42,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 1.740295214619,
          "naive_default_probability": 0.040903596951,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 10,
        "value": 1.815766912733,
        "value_label": "1.8158 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.8158 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.4,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 1.815766912733,
          "naive_default_probability": 0.034703067411,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 11,
        "value": 1.891238610846,
        "value_label": "1.8912 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.8912 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.38,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 1.891238610846,
          "naive_default_probability": 0.029296249676,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 12,
        "value": 1.966710308959,
        "value_label": "1.9667 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.9667 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.36,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 1.966710308959,
          "naive_default_probability": 0.024608308865,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 13,
        "value": 2.042182007072,
        "value_label": "2.0422 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.0422 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.34,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.042182007072,
          "naive_default_probability": 0.020566740298,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 14,
        "value": 2.117653705185,
        "value_label": "2.1177 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.1177 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.32,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.117653705185,
          "naive_default_probability": 0.017102203139,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 15,
        "value": 2.193125403299,
        "value_label": "2.1931 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.1931 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.3,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.193125403299,
          "naive_default_probability": 0.014149172607,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 16,
        "value": 2.268597101412,
        "value_label": "2.2686 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.2686 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.28,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.268597101412,
          "naive_default_probability": 0.011646419025,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 17,
        "value": 2.344068799525,
        "value_label": "2.3441 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.3441 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.26,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.344068799525,
          "naive_default_probability": 0.009537326234,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 18,
        "value": 2.419540497638,
        "value_label": "2.4195 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4195 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.24,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.419540497638,
          "naive_default_probability": 0.007770065113,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 19,
        "value": 2.495012195752,
        "value_label": "2.4950 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4950 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.22,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.495012195752,
          "naive_default_probability": 0.006297640055,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 20,
        "value": 2.570483893865,
        "value_label": "2.5705 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5705 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.2,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.570483893865,
          "naive_default_probability": 0.005077827449,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 21,
        "value": 2.645955591978,
        "value_label": "2.6460 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.6460 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.18,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.645955591978,
          "naive_default_probability": 0.004073025487,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 22,
        "value": 2.721427290091,
        "value_label": "2.7214 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7214 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.16,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.721427290091,
          "naive_default_probability": 0.003250034134,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 23,
        "value": 2.796898988204,
        "value_label": "2.7969 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7969 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.14,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.796898988204,
          "naive_default_probability": 0.002579783073,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 24,
        "value": 2.872370686318,
        "value_label": "2.8724 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.8724 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.12,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.872370686318,
          "naive_default_probability": 0.00203702388,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 25,
        "value": 2.947842384431,
        "value_label": "2.9478 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.9478 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.1,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.947842384431,
          "naive_default_probability": 0.001600000868,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 26,
        "value": 3.023314082544,
        "value_label": "3.0233 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.0233 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.023314082544,
          "naive_default_probability": 0.001250113017,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 27,
        "value": 3.098785780657,
        "value_label": "3.0988 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.0988 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.06,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.098785780657,
          "naive_default_probability": 0.000971577322,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 28,
        "value": 3.17425747877,
        "value_label": "3.1743 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.1743 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.04,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.17425747877,
          "naive_default_probability": 0.000751101842,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 29,
        "value": 3.249729176884,
        "value_label": "3.2497 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.2497 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.02,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.249729176884,
          "naive_default_probability": 0.000577574797,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 30,
        "value": 3.325200874997,
        "value_label": "3.3252 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.3252 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.0,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.325200874997,
          "naive_default_probability": 0.000441774261,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 31,
        "value": 3.40067257311,
        "value_label": "3.4007 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.4007 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.02,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.40067257311,
          "naive_default_probability": 0.000336101455,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 32,
        "value": 3.476144271223,
        "value_label": "3.4761 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.4761 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.04,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.476144271223,
          "naive_default_probability": 0.000254339281,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 33,
        "value": 3.551615969336,
        "value_label": "3.5516 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.5516 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.06,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.551615969336,
          "naive_default_probability": 0.000191436614,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 34,
        "value": 3.62708766745,
        "value_label": "3.6271 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.6271 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.62708766745,
          "naive_default_probability": 0.000143317997,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 35,
        "value": 3.702559365563,
        "value_label": "3.7026 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.7026 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.1,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.702559365563,
          "naive_default_probability": 0.000106717698,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 36,
        "value": 3.778031063676,
        "value_label": "3.7780 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.7780 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.12,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.778031063676,
          "naive_default_probability": 7.9036583e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 37,
        "value": 3.853502761789,
        "value_label": "3.8535 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.8535 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.14,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.853502761789,
          "naive_default_probability": 5.8219975e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 38,
        "value": 3.928974459902,
        "value_label": "3.9290 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.9290 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.16,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.928974459902,
          "naive_default_probability": 4.2654449e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 39,
        "value": 4.004446158016,
        "value_label": "4.0044 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.0044 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.18,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.004446158016,
          "naive_default_probability": 3.1081473e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 40,
        "value": 4.079917856129,
        "value_label": "4.0799 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.0799 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.2,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.079917856129,
          "naive_default_probability": 2.2525809e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 41,
        "value": 4.155389554242,
        "value_label": "4.1554 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.1554 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.22,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.155389554242,
          "naive_default_probability": 1.6236689e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 42,
        "value": 4.230861252355,
        "value_label": "4.2309 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.2309 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.24,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.230861252355,
          "naive_default_probability": 1.1639912e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 43,
        "value": 4.306332950469,
        "value_label": "4.3063 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.3063 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.26,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.306332950469,
          "naive_default_probability": 8.299158e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 44,
        "value": 4.381804648582,
        "value_label": "4.3818 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.3818 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.28,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.381804648582,
          "naive_default_probability": 5.885016e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 45,
        "value": 4.457276346695,
        "value_label": "4.4573 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.4573 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.3,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.457276346695,
          "naive_default_probability": 4.150378e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 46,
        "value": 4.532748044808,
        "value_label": "4.5327 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.5327 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.32,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.532748044808,
          "naive_default_probability": 2.911062e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 47,
        "value": 4.608219742921,
        "value_label": "4.6082 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.6082 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.34,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.608219742921,
          "naive_default_probability": 2.030657e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 48,
        "value": 4.683691441035,
        "value_label": "4.6837 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.6837 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.36,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.683691441035,
          "naive_default_probability": 1.40877e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 49,
        "value": 4.759163139148,
        "value_label": "4.7592 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.7592 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.38,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.759163139148,
          "naive_default_probability": 9.71986e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 50,
        "value": 4.834634837261,
        "value_label": "4.8346 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.8346 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.4,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.834634837261,
          "naive_default_probability": 6.66951e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 51,
        "value": 4.910106535374,
        "value_label": "4.9101 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.9101 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.42,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.910106535374,
          "naive_default_probability": 4.55135e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 52,
        "value": 4.985578233487,
        "value_label": "4.9856 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.9856 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.44,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.985578233487,
          "naive_default_probability": 3.08884e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 53,
        "value": 5.061049931601,
        "value_label": "5.0610 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.0610 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.46,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 5.061049931601,
          "naive_default_probability": 2.08477e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 54,
        "value": 5.136521629714,
        "value_label": "5.1365 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.1365 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.48,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 5.136521629714,
          "naive_default_probability": 1.39935e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 55,
        "value": 5.211993327827,
        "value_label": "5.2120 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.2120 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.5,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 5.211993327827,
          "naive_default_probability": 9.3411e-08,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 56,
        "value": 5.28746502594,
        "value_label": "5.2875 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.2875 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.52,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 5.28746502594,
          "naive_default_probability": 6.2012e-08,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 57,
        "value": 5.362936724053,
        "value_label": "5.3629 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.3629 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.54,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 5.362936724053,
          "naive_default_probability": 4.094e-08,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 58,
        "value": 5.438408422167,
        "value_label": "5.4384 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.4384 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.56,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 5.438408422167,
          "naive_default_probability": 2.6879e-08,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 59,
        "value": 5.51388012028,
        "value_label": "5.5139 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.5139 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.58,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 5.51388012028,
          "naive_default_probability": 1.755e-08,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 60,
        "value": 5.589351818393,
        "value_label": "5.5894 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.5894 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.6,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 5.589351818393,
          "naive_default_probability": 1.1396e-08,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      }
    ]
  },
  {
    "name": "Sensitivity",
    "description": "Synthetic sensitivity sweep; only declared fields change while the topic contract remains fixed.",
    "canonical_step": 30,
    "summary": {
      "focus_step": 30,
      "focus_kind": "comparison",
      "canonical_output_match": false,
      "state_counts": {
        "calculated": 61
      },
      "value_min": 2.289691061616,
      "value_max": 7.00009514622,
      "segments": [
        {
          "start_step": 0,
          "end_step": 60,
          "state": "calculated",
          "decision": "bharath-shumway-naive-approximation",
          "start_value_label": "7.0001 sigma",
          "end_value_label": "2.2897 sigma"
        }
      ]
    },
    "states": [
      {
        "step": 0,
        "value": 7.00009514622,
        "value_label": "7.0001 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 7.0001 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.25
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 7.00009514622,
          "naive_default_probability": 1e-12,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 1,
        "value": 6.449301031197,
        "value_label": "6.4493 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 6.4493 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.295833333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 6.449301031197,
          "naive_default_probability": 5.6e-11,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 2,
        "value": 6.014437615315,
        "value_label": "6.0144 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 6.0144 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.341666666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 6.014437615315,
          "naive_default_probability": 9.03e-10,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 3,
        "value": 5.660026780684,
        "value_label": "5.6600 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.6600 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.3875
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 5.660026780684,
          "naive_default_probability": 7.567e-09,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 4,
        "value": 5.364128731001,
        "value_label": "5.3641 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.3641 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.433333333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 5.364128731001,
          "naive_default_probability": 4.067e-08,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 5,
        "value": 5.11235193231,
        "value_label": "5.1124 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.1124 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.479166666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 5.11235193231,
          "naive_default_probability": 1.59086e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 6,
        "value": 4.89481296795,
        "value_label": "4.8948 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.8948 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.525
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.89481296795,
          "naive_default_probability": 4.91996e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 7,
        "value": 4.704470194883,
        "value_label": "4.7045 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.7045 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.570833333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.704470194883,
          "naive_default_probability": 1.27263e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 8,
        "value": 4.536153118748,
        "value_label": "4.5362 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.5362 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.616666666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.536153118748,
          "naive_default_probability": 2.86448e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 9,
        "value": 4.38596838625,
        "value_label": "4.3860 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.3860 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.6625
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.38596838625,
          "naive_default_probability": 5.773545e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 10,
        "value": 4.250921059778,
        "value_label": "4.2509 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.2509 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.708333333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.250921059778,
          "naive_default_probability": 1.064466e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 11,
        "value": 4.128664661278,
        "value_label": "4.1287 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.1287 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.754166666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.128664661278,
          "naive_default_probability": 1.8243805e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 12,
        "value": 4.017331254143,
        "value_label": "4.0173 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.0173 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.8
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 4.017331254143,
          "naive_default_probability": 2.9430478e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 13,
        "value": 3.915412941163,
        "value_label": "3.9154 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.9154 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.845833333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.915412941163,
          "naive_default_probability": 4.5124803e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 14,
        "value": 3.821677351107,
        "value_label": "3.8217 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.8217 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.891666666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.821677351107,
          "naive_default_probability": 6.6273519e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 15,
        "value": 3.735106164567,
        "value_label": "3.7351 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.7351 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.9375
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.735106164567,
          "naive_default_probability": 9.3818007e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 16,
        "value": 3.654849607488,
        "value_label": "3.6548 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.6548 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 0.983333333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.654849607488,
          "naive_default_probability": 0.000128666391,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 17,
        "value": 3.580192232268,
        "value_label": "3.5802 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.5802 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.029166666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.580192232268,
          "naive_default_probability": 0.000171670764,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 18,
        "value": 3.510526820745,
        "value_label": "3.5105 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.5105 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.075
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.510526820745,
          "naive_default_probability": 0.000223609845,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 19,
        "value": 3.445334225418,
        "value_label": "3.4453 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.4453 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.120833333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.445334225418,
          "naive_default_probability": 0.000285176845,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 20,
        "value": 3.384167615677,
        "value_label": "3.3842 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.3842 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.166666666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.384167615677,
          "naive_default_probability": 0.000356972019,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 21,
        "value": 3.326640035168,
        "value_label": "3.3266 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.3266 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.2125
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.326640035168,
          "naive_default_probability": 0.000439499207,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 22,
        "value": 3.272414478228,
        "value_label": "3.2724 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.2724 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.258333333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.272414478228,
          "naive_default_probability": 0.000533165636,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 23,
        "value": 3.221195904209,
        "value_label": "3.2212 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.2212 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.304166666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.221195904209,
          "naive_default_probability": 0.000638284276,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 24,
        "value": 3.172724757878,
        "value_label": "3.1727 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.1727 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.35
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.172724757878,
          "naive_default_probability": 0.000755078093,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 25,
        "value": 3.126771671419,
        "value_label": "3.1268 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.1268 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.395833333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.126771671419,
          "naive_default_probability": 0.000883685649,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 26,
        "value": 3.083133101632,
        "value_label": "3.0831 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.0831 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.441666666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.083133101632,
          "naive_default_probability": 0.001024167587,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 27,
        "value": 3.041627713346,
        "value_label": "3.0416 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.0416 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.4875
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.041627713346,
          "naive_default_probability": 0.001176513605,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 28,
        "value": 3.002093362803,
        "value_label": "3.0021 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.0021 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.533333333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 3.002093362803,
          "naive_default_probability": 0.001340649643,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 29,
        "value": 2.964384566876,
        "value_label": "2.9644 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.9644 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.579166666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.964384566876,
          "naive_default_probability": 0.001516445027,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 30,
        "value": 2.928370368289,
        "value_label": "2.9284 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.9284 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.625
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.928370368289,
          "naive_default_probability": 0.001703719435,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 31,
        "value": 2.89393252568,
        "value_label": "2.8939 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.8939 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.670833333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.89393252568,
          "naive_default_probability": 0.001902249535,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 32,
        "value": 2.860963971673,
        "value_label": "2.8610 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.8610 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.716666666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.860963971673,
          "naive_default_probability": 0.00211177523,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 33,
        "value": 2.829367493304,
        "value_label": "2.8294 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.8294 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.7625
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.829367493304,
          "naive_default_probability": 0.002332005458,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 34,
        "value": 2.799054597896,
        "value_label": "2.7991 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7991 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.808333333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.799054597896,
          "naive_default_probability": 0.002562623527,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 35,
        "value": 2.769944534347,
        "value_label": "2.7699 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7699 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.854166666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.769944534347,
          "naive_default_probability": 0.002803291963,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 36,
        "value": 2.741963445308,
        "value_label": "2.7420 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7420 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.9
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.741963445308,
          "naive_default_probability": 0.003053656893,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 37,
        "value": 2.715043630039,
        "value_label": "2.7150 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7150 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.945833333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.715043630039,
          "naive_default_probability": 0.003313351978,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 38,
        "value": 2.689122901289,
        "value_label": "2.6891 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.6891 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.991666666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.689122901289,
          "naive_default_probability": 0.003582001903,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 39,
        "value": 2.664144022343,
        "value_label": "2.6641 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.6641 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.0375
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.664144022343,
          "naive_default_probability": 0.003859225468,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 40,
        "value": 2.640054212697,
        "value_label": "2.6401 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.6401 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.083333333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.640054212697,
          "naive_default_probability": 0.004144638304,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 41,
        "value": 2.616804712704,
        "value_label": "2.6168 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.6168 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.129166666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.616804712704,
          "naive_default_probability": 0.004437855238,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 42,
        "value": 2.594350399031,
        "value_label": "2.5944 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5944 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.175
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.594350399031,
          "naive_default_probability": 0.00473849234,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 43,
        "value": 2.572649444098,
        "value_label": "2.5726 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5726 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.220833333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.572649444098,
          "naive_default_probability": 0.005046168693,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 44,
        "value": 2.551663013659,
        "value_label": "2.5517 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5517 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.266666666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.551663013659,
          "naive_default_probability": 0.00536050789,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 45,
        "value": 2.531354997582,
        "value_label": "2.5314 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5314 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.3125
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.531354997582,
          "naive_default_probability": 0.005681139307,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 46,
        "value": 2.51169176962,
        "value_label": "2.5117 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5117 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.358333333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.51169176962,
          "naive_default_probability": 0.006007699166,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 47,
        "value": 2.492641972536,
        "value_label": "2.4926 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4926 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.404166666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.492641972536,
          "naive_default_probability": 0.00633983141,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 48,
        "value": 2.474176325506,
        "value_label": "2.4742 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4742 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.45
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.474176325506,
          "naive_default_probability": 0.006677188419,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 49,
        "value": 2.456267451093,
        "value_label": "2.4563 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4563 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.495833333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.456267451093,
          "naive_default_probability": 0.007019431581,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 50,
        "value": 2.438889719518,
        "value_label": "2.4389 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4389 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.541666666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.438889719518,
          "naive_default_probability": 0.007366231727,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 51,
        "value": 2.422019108193,
        "value_label": "2.4220 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4220 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.5875
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.422019108193,
          "naive_default_probability": 0.007717269468,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 52,
        "value": 2.4056330748,
        "value_label": "2.4056 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4056 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.633333333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.4056330748,
          "naive_default_probability": 0.008072235426,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 53,
        "value": 2.389710442395,
        "value_label": "2.3897 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.3897 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.679166666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.389710442395,
          "naive_default_probability": 0.008430830383,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 54,
        "value": 2.374231295203,
        "value_label": "2.3742 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.3742 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.725
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.374231295203,
          "naive_default_probability": 0.008792765359,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 55,
        "value": 2.35917688397,
        "value_label": "2.3592 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.3592 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.770833333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.35917688397,
          "naive_default_probability": 0.009157761626,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 56,
        "value": 2.344529539836,
        "value_label": "2.3445 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.3445 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.816666666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.344529539836,
          "naive_default_probability": 0.009525550667,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 57,
        "value": 2.330272595839,
        "value_label": "2.3303 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.3303 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.8625
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.330272595839,
          "naive_default_probability": 0.009895874096,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 58,
        "value": 2.316390315283,
        "value_label": "2.3164 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.3164 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.908333333333
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.316390315283,
          "naive_default_probability": 0.010268483532,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 59,
        "value": 2.302867826242,
        "value_label": "2.3029 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.3029 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 2.954166666667
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.302867826242,
          "naive_default_probability": 0.010643140442,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 60,
        "value": 2.289691061616,
        "value_label": "2.2897 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.2897 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.08,
          "horizon_years": 3.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.265,
          "naive_distance_to_default": 2.289691061616,
          "naive_default_probability": 0.011019615967,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      }
    ]
  },
  {
    "name": "Scale or horizon",
    "description": "Synthetic scale or horizon sweep; only declared fields change while the topic contract remains fixed.",
    "canonical_step": 30,
    "summary": {
      "focus_step": 30,
      "focus_kind": "comparison",
      "canonical_output_match": false,
      "state_counts": {
        "calculated": 61
      },
      "value_min": 0.827425527032,
      "value_max": 7.419327049723,
      "segments": [
        {
          "start_step": 0,
          "end_step": 60,
          "state": "calculated",
          "decision": "bharath-shumway-naive-approximation",
          "start_value_label": "7.4193 sigma",
          "end_value_label": "0.8274 sigma"
        }
      ]
    },
    "states": [
      {
        "step": 0,
        "value": 7.419327049723,
        "value_label": "7.4193 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 7.4193 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 160.0,
          "equity_volatility": 0.1,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 280.0,
          "naive_debt_volatility": 0.075,
          "naive_asset_volatility": 0.085714285714,
          "naive_distance_to_default": 7.419327049723,
          "naive_default_probability": 0.0,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 1,
        "value": 6.641204452071,
        "value_label": "6.6412 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 6.6412 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 158.333333333333,
          "equity_volatility": 0.118333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 278.333333333333,
          "naive_debt_volatility": 0.079583333333,
          "naive_asset_volatility": 0.09628992016,
          "naive_distance_to_default": 6.641204452071,
          "naive_default_probability": 1.6e-11,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 2,
        "value": 6.012611624566,
        "value_label": "6.0126 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 6.0126 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 156.666666666667,
          "equity_volatility": 0.136666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 276.666666666667,
          "naive_debt_volatility": 0.084166666667,
          "naive_asset_volatility": 0.106937751004,
          "naive_distance_to_default": 6.012611624566,
          "naive_default_probability": 9.13e-10,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 3,
        "value": 5.494043383439,
        "value_label": "5.4940 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.4940 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 155.0,
          "equity_volatility": 0.155,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 275.0,
          "naive_debt_volatility": 0.08875,
          "naive_asset_volatility": 0.117659090909,
          "naive_distance_to_default": 5.494043383439,
          "naive_default_probability": 1.9642e-08,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 4,
        "value": 5.058783474518,
        "value_label": "5.0588 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 5.0588 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 153.333333333333,
          "equity_volatility": 0.173333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 273.333333333333,
          "naive_debt_volatility": 0.093333333333,
          "naive_asset_volatility": 0.128455284553,
          "naive_distance_to_default": 5.058783474518,
          "naive_default_probability": 2.1097e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 5,
        "value": 4.688116892029,
        "value_label": "4.6881 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.6881 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 151.666666666667,
          "equity_volatility": 0.191666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 271.666666666667,
          "naive_debt_volatility": 0.097916666667,
          "naive_asset_volatility": 0.139327709611,
          "naive_distance_to_default": 4.688116892029,
          "naive_default_probability": 1.378653e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 6,
        "value": 4.368543169609,
        "value_label": "4.3685 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.3685 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 150.0,
          "equity_volatility": 0.21,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 270.0,
          "naive_debt_volatility": 0.1025,
          "naive_asset_volatility": 0.150277777778,
          "naive_distance_to_default": 4.368543169609,
          "naive_default_probability": 6.253905e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 7,
        "value": 4.090078508627,
        "value_label": "4.0901 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.0901 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 148.333333333333,
          "equity_volatility": 0.228333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 268.333333333333,
          "naive_debt_volatility": 0.107083333333,
          "naive_asset_volatility": 0.161306935818,
          "naive_distance_to_default": 4.090078508627,
          "naive_default_probability": 2.156136e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 8,
        "value": 3.845180747898,
        "value_label": "3.8452 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.8452 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 146.666666666667,
          "equity_volatility": 0.246666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 266.666666666667,
          "naive_debt_volatility": 0.111666666667,
          "naive_asset_volatility": 0.172416666667,
          "naive_distance_to_default": 3.845180747898,
          "naive_default_probability": 6.0231805e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 9,
        "value": 3.62804597221,
        "value_label": "3.6280 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.6280 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 145.0,
          "equity_volatility": 0.265,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 265.0,
          "naive_debt_volatility": 0.11625,
          "naive_asset_volatility": 0.183608490566,
          "naive_distance_to_default": 3.62804597221,
          "naive_default_probability": 0.000142787209,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 10,
        "value": 3.434135036966,
        "value_label": "3.4341 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.4341 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 143.333333333333,
          "equity_volatility": 0.283333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 263.333333333333,
          "naive_debt_volatility": 0.120833333333,
          "naive_asset_volatility": 0.194883966245,
          "naive_distance_to_default": 3.434135036966,
          "naive_default_probability": 0.000297223988,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 11,
        "value": 3.259846861264,
        "value_label": "3.2598 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.2598 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 141.666666666667,
          "equity_volatility": 0.301666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 261.666666666667,
          "naive_debt_volatility": 0.125416666667,
          "naive_asset_volatility": 0.206244692144,
          "naive_distance_to_default": 3.259846861264,
          "naive_default_probability": 0.000557361919,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 12,
        "value": 3.102288019045,
        "value_label": "3.1023 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.1023 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 140.0,
          "equity_volatility": 0.32,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 260.0,
          "naive_debt_volatility": 0.13,
          "naive_asset_volatility": 0.217692307692,
          "naive_distance_to_default": 3.102288019045,
          "naive_default_probability": 0.000960155121,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 13,
        "value": 2.959107064166,
        "value_label": "2.9591 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.9591 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 138.333333333333,
          "equity_volatility": 0.338333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 258.333333333333,
          "naive_debt_volatility": 0.134583333333,
          "naive_asset_volatility": 0.229228494624,
          "naive_distance_to_default": 2.959107064166,
          "naive_default_probability": 0.001542659447,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 14,
        "value": 2.82837332034,
        "value_label": "2.8284 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.8284 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 136.666666666667,
          "equity_volatility": 0.356666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 256.666666666667,
          "naive_debt_volatility": 0.139166666667,
          "naive_asset_volatility": 0.240854978355,
          "naive_distance_to_default": 2.82837332034,
          "naive_default_probability": 0.002339260663,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 15,
        "value": 2.708486809498,
        "value_label": "2.7085 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7085 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 135.0,
          "equity_volatility": 0.375,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 255.0,
          "naive_debt_volatility": 0.14375,
          "naive_asset_volatility": 0.252573529412,
          "naive_distance_to_default": 2.708486809498,
          "naive_default_probability": 0.003379539942,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 16,
        "value": 2.598110369357,
        "value_label": "2.5981 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5981 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 133.333333333333,
          "equity_volatility": 0.393333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 253.333333333333,
          "naive_debt_volatility": 0.148333333333,
          "naive_asset_volatility": 0.264385964912,
          "naive_distance_to_default": 2.598110369357,
          "naive_default_probability": 0.004686917958,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 17,
        "value": 2.496117834488,
        "value_label": "2.4961 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4961 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 131.666666666667,
          "equity_volatility": 0.411666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 251.666666666667,
          "naive_debt_volatility": 0.152916666667,
          "naive_asset_volatility": 0.27629415011,
          "naive_distance_to_default": 2.496117834488,
          "naive_default_probability": 0.006278044204,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 18,
        "value": 2.401554014591,
        "value_label": "2.4016 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4016 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 130.0,
          "equity_volatility": 0.43,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 250.0,
          "naive_debt_volatility": 0.1575,
          "naive_asset_volatility": 0.2883,
          "naive_distance_to_default": 2.401554014591,
          "naive_default_probability": 0.008162799329,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 19,
        "value": 2.313603451281,
        "value_label": "2.3136 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.3136 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 128.333333333333,
          "equity_volatility": 0.448333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 248.333333333333,
          "naive_debt_volatility": 0.162083333333,
          "naive_asset_volatility": 0.300405480984,
          "naive_distance_to_default": 2.313603451281,
          "naive_default_probability": 0.010344742103,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 20,
        "value": 2.231565786375,
        "value_label": "2.2316 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.2316 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 126.666666666667,
          "equity_volatility": 0.466666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 246.666666666667,
          "naive_debt_volatility": 0.166666666667,
          "naive_asset_volatility": 0.312612612613,
          "naive_distance_to_default": 2.231565786375,
          "naive_default_probability": 0.012821837506,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 21,
        "value": 2.154836165212,
        "value_label": "2.1548 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.1548 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 125.0,
          "equity_volatility": 0.485,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 245.0,
          "naive_debt_volatility": 0.17125,
          "naive_asset_volatility": 0.324923469388,
          "naive_distance_to_default": 2.154836165212,
          "naive_default_probability": 0.01558732855,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 22,
        "value": 2.082889514001,
        "value_label": "2.0829 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.0829 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 123.333333333333,
          "equity_volatility": 0.503333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 243.333333333333,
          "naive_debt_volatility": 0.175833333333,
          "naive_asset_volatility": 0.337340182648,
          "naive_distance_to_default": 2.082889514001,
          "naive_default_probability": 0.018630647824,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 23,
        "value": 2.01526782641,
        "value_label": "2.0153 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.0153 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 121.666666666667,
          "equity_volatility": 0.521666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 241.666666666667,
          "naive_debt_volatility": 0.180416666667,
          "naive_asset_volatility": 0.349864942529,
          "naive_distance_to_default": 2.01526782641,
          "naive_default_probability": 0.021938297059,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 24,
        "value": 1.951569808441,
        "value_label": "1.9516 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.9516 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 120.0,
          "equity_volatility": 0.54,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 240.0,
          "naive_debt_volatility": 0.185,
          "naive_asset_volatility": 0.3625,
          "naive_distance_to_default": 1.951569808441,
          "naive_default_probability": 0.025494650329,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 25,
        "value": 1.891442386758,
        "value_label": "1.8914 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.8914 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 118.333333333333,
          "equity_volatility": 0.558333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 238.333333333333,
          "naive_debt_volatility": 0.189583333333,
          "naive_asset_volatility": 0.375247668998,
          "naive_distance_to_default": 1.891442386758,
          "naive_default_probability": 0.029282657451,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 26,
        "value": 1.834573700864,
        "value_label": "1.8346 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.8346 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 116.666666666667,
          "equity_volatility": 0.576666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 236.666666666667,
          "naive_debt_volatility": 0.194166666667,
          "naive_asset_volatility": 0.388110328638,
          "naive_distance_to_default": 1.834573700864,
          "naive_default_probability": 0.033284439176,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 27,
        "value": 1.780687285435,
        "value_label": "1.7807 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.7807 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 115.0,
          "equity_volatility": 0.595,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 235.0,
          "naive_debt_volatility": 0.19875,
          "naive_asset_volatility": 0.401090425532,
          "naive_distance_to_default": 1.780687285435,
          "naive_default_probability": 0.037481775701,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 28,
        "value": 1.729537213744,
        "value_label": "1.7295 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.7295 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 113.333333333333,
          "equity_volatility": 0.613333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 233.333333333333,
          "naive_debt_volatility": 0.203333333333,
          "naive_asset_volatility": 0.41419047619,
          "naive_distance_to_default": 1.729537213744,
          "naive_default_probability": 0.041856496076,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 29,
        "value": 1.680904022184,
        "value_label": "1.6809 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.6809 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 111.666666666667,
          "equity_volatility": 0.631666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 231.666666666667,
          "naive_debt_volatility": 0.207916666667,
          "naive_asset_volatility": 0.427413069544,
          "naive_distance_to_default": 1.680904022184,
          "naive_default_probability": 0.046390779296,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 30,
        "value": 1.63459127343,
        "value_label": "1.6346 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.6346 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 110.0,
          "equity_volatility": 0.65,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 230.0,
          "naive_debt_volatility": 0.2125,
          "naive_asset_volatility": 0.440760869565,
          "naive_distance_to_default": 1.63459127343,
          "naive_default_probability": 0.051067379118,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 31,
        "value": 1.590422644782,
        "value_label": "1.5904 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.5904 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 108.333333333333,
          "equity_volatility": 0.668333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 228.333333333333,
          "naive_debt_volatility": 0.217083333333,
          "naive_asset_volatility": 0.454236618005,
          "naive_distance_to_default": 1.590422644782,
          "naive_default_probability": 0.055869784678,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 32,
        "value": 1.548239450702,
        "value_label": "1.5482 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.5482 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 106.666666666667,
          "equity_volatility": 0.686666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 226.666666666667,
          "naive_debt_volatility": 0.221666666667,
          "naive_asset_volatility": 0.467843137255,
          "naive_distance_to_default": 1.548239450702,
          "naive_default_probability": 0.060782328195,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 33,
        "value": 1.507898526198,
        "value_label": "1.5079 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.5079 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 105.0,
          "equity_volatility": 0.705,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 225.0,
          "naive_debt_volatility": 0.22625,
          "naive_asset_volatility": 0.481583333333,
          "naive_distance_to_default": 1.507898526198,
          "naive_default_probability": 0.06579024996,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 34,
        "value": 1.469270411566,
        "value_label": "1.4693 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.4693 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 103.333333333333,
          "equity_volatility": 0.723333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 223.333333333333,
          "naive_debt_volatility": 0.230833333333,
          "naive_asset_volatility": 0.495460199005,
          "naive_distance_to_default": 1.469270411566,
          "naive_default_probability": 0.070879729434,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 35,
        "value": 1.432237789998,
        "value_label": "1.4322 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.4322 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 101.666666666667,
          "equity_volatility": 0.741666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 221.666666666667,
          "naive_debt_volatility": 0.235416666667,
          "naive_asset_volatility": 0.509476817043,
          "naive_distance_to_default": 1.432237789998,
          "naive_default_probability": 0.076037890028,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 36,
        "value": 1.396694138322,
        "value_label": "1.3967 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.3967 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 100.0,
          "equity_volatility": 0.76,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 220.0,
          "naive_debt_volatility": 0.24,
          "naive_asset_volatility": 0.523636363636,
          "naive_distance_to_default": 1.396694138322,
          "naive_default_probability": 0.08125278382,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 37,
        "value": 1.362542558188,
        "value_label": "1.3625 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.3625 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 98.333333333333,
          "equity_volatility": 0.778333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 218.333333333333,
          "naive_debt_volatility": 0.244583333333,
          "naive_asset_volatility": 0.537942111959,
          "naive_distance_to_default": 1.362542558188,
          "naive_default_probability": 0.086513361387,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 38,
        "value": 1.329694760662,
        "value_label": "1.3297 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.3297 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 96.666666666667,
          "equity_volatility": 0.796666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 216.666666666667,
          "naive_debt_volatility": 0.249166666667,
          "naive_asset_volatility": 0.552397435897,
          "naive_distance_to_default": 1.329694760662,
          "naive_default_probability": 0.0918094309,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 39,
        "value": 1.298070181797,
        "value_label": "1.2981 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.2981 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 95.0,
          "equity_volatility": 0.815,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 215.0,
          "naive_debt_volatility": 0.25375,
          "naive_asset_volatility": 0.567005813953,
          "naive_distance_to_default": 1.298070181797,
          "naive_default_probability": 0.097131609792,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 40,
        "value": 1.267595210472,
        "value_label": "1.2676 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.2676 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 93.333333333333,
          "equity_volatility": 0.833333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 213.333333333333,
          "naive_debt_volatility": 0.258333333333,
          "naive_asset_volatility": 0.581770833333,
          "naive_distance_to_default": 1.267595210472,
          "naive_default_probability": 0.10247127161,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 41,
        "value": 1.238202512894,
        "value_label": "1.2382 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.2382 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 91.666666666667,
          "equity_volatility": 0.851666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 211.666666666667,
          "naive_debt_volatility": 0.262916666667,
          "naive_asset_volatility": 0.596696194226,
          "naive_distance_to_default": 1.238202512894,
          "naive_default_probability": 0.107820490014,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 42,
        "value": 1.20983044063,
        "value_label": "1.2098 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.2098 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 90.0,
          "equity_volatility": 0.87,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 210.0,
          "naive_debt_volatility": 0.2675,
          "naive_asset_volatility": 0.611785714286,
          "naive_distance_to_default": 1.20983044063,
          "naive_default_probability": 0.113171981468,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 43,
        "value": 1.182422511168,
        "value_label": "1.1824 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.1824 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 88.333333333333,
          "equity_volatility": 0.888333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 208.333333333333,
          "naive_debt_volatility": 0.272083333333,
          "naive_asset_volatility": 0.627043333333,
          "naive_distance_to_default": 1.182422511168,
          "naive_default_probability": 0.118519047696,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 44,
        "value": 1.155926951709,
        "value_label": "1.1559 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.1559 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 86.666666666667,
          "equity_volatility": 0.906666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 206.666666666667,
          "naive_debt_volatility": 0.276666666667,
          "naive_asset_volatility": 0.64247311828,
          "naive_distance_to_default": 1.155926951709,
          "naive_default_probability": 0.123855518706,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 45,
        "value": 1.130296298346,
        "value_label": "1.1303 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.1303 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 85.0,
          "equity_volatility": 0.925,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 205.0,
          "naive_debt_volatility": 0.28125,
          "naive_asset_volatility": 0.658079268293,
          "naive_distance_to_default": 1.130296298346,
          "naive_default_probability": 0.12917569691,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 46,
        "value": 1.105487044035,
        "value_label": "1.1055 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.1055 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 83.333333333333,
          "equity_volatility": 0.943333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 203.333333333333,
          "naive_debt_volatility": 0.285833333333,
          "naive_asset_volatility": 0.673866120219,
          "naive_distance_to_default": 1.105487044035,
          "naive_default_probability": 0.134474302642,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 47,
        "value": 1.081459329736,
        "value_label": "1.0815 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.0815 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 81.666666666667,
          "equity_volatility": 0.961666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 201.666666666667,
          "naive_debt_volatility": 0.290416666667,
          "naive_asset_volatility": 0.68983815427,
          "naive_distance_to_default": 1.081459329736,
          "naive_default_probability": 0.139746421251,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 48,
        "value": 1.058176674043,
        "value_label": "1.0582 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.0582 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 80.0,
          "equity_volatility": 0.98,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 200.0,
          "naive_debt_volatility": 0.295,
          "naive_asset_volatility": 0.706,
          "naive_distance_to_default": 1.058176674043,
          "naive_default_probability": 0.144987451778,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 49,
        "value": 1.035605737337,
        "value_label": "1.0356 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.0356 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 78.333333333333,
          "equity_volatility": 0.998333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 198.333333333333,
          "naive_debt_volatility": 0.299583333333,
          "naive_asset_volatility": 0.722356442577,
          "naive_distance_to_default": 1.035605737337,
          "naive_default_probability": 0.150193057132,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 50,
        "value": 1.013716117161,
        "value_label": "1.0137 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.0137 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 76.666666666667,
          "equity_volatility": 1.016666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 196.666666666667,
          "naive_debt_volatility": 0.304166666667,
          "naive_asset_volatility": 0.738912429379,
          "naive_distance_to_default": 1.013716117161,
          "naive_default_probability": 0.155359115615,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 51,
        "value": 0.992480172098,
        "value_label": "0.9925 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.9925 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 75.0,
          "equity_volatility": 1.035,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 195.0,
          "naive_debt_volatility": 0.30875,
          "naive_asset_volatility": 0.755673076923,
          "naive_distance_to_default": 0.992480172098,
          "naive_default_probability": 0.16048167353,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 52,
        "value": 0.971872871948,
        "value_label": "0.9719 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.9719 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 73.333333333333,
          "equity_volatility": 1.053333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 193.333333333333,
          "naive_debt_volatility": 0.313333333333,
          "naive_asset_volatility": 0.772643678161,
          "naive_distance_to_default": 0.971872871948,
          "naive_default_probability": 0.165556898589,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 53,
        "value": 0.951871672462,
        "value_label": "0.9519 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.9519 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 71.666666666667,
          "equity_volatility": 1.071666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 191.666666666667,
          "naive_debt_volatility": 0.317916666667,
          "naive_asset_volatility": 0.789829710145,
          "naive_distance_to_default": 0.951871672462,
          "naive_default_probability": 0.17058103375,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 54,
        "value": 0.932456413315,
        "value_label": "0.9325 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.9325 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 70.0,
          "equity_volatility": 1.09,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 190.0,
          "naive_debt_volatility": 0.3225,
          "naive_asset_volatility": 0.807236842105,
          "naive_distance_to_default": 0.932456413315,
          "naive_default_probability": 0.175550351075,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 55,
        "value": 0.913609238444,
        "value_label": "0.9136 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.9136 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 68.333333333333,
          "equity_volatility": 1.108333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 188.333333333333,
          "naive_debt_volatility": 0.327083333333,
          "naive_asset_volatility": 0.824870943953,
          "naive_distance_to_default": 0.913609238444,
          "naive_default_probability": 0.180461105131,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 56,
        "value": 0.895314538244,
        "value_label": "0.8953 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.8953 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 66.666666666667,
          "equity_volatility": 1.126666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 186.666666666667,
          "naive_debt_volatility": 0.331666666667,
          "naive_asset_volatility": 0.842738095238,
          "naive_distance_to_default": 0.895314538244,
          "naive_default_probability": 0.185309485414,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 57,
        "value": 0.877558913542,
        "value_label": "0.8776 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.8776 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 65.0,
          "equity_volatility": 1.145,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 185.0,
          "naive_debt_volatility": 0.33625,
          "naive_asset_volatility": 0.860844594595,
          "naive_distance_to_default": 0.877558913542,
          "naive_default_probability": 0.190091567184,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 58,
        "value": 0.860331161702,
        "value_label": "0.8603 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.8603 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 63.333333333333,
          "equity_volatility": 1.163333333333,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 183.333333333333,
          "naive_debt_volatility": 0.340833333333,
          "naive_asset_volatility": 0.879196969697,
          "naive_distance_to_default": 0.860331161702,
          "naive_default_probability": 0.194803260042,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 59,
        "value": 0.843622285632,
        "value_label": "0.8436 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.8436 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 61.666666666667,
          "equity_volatility": 1.181666666667,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 181.666666666667,
          "naive_debt_volatility": 0.345416666667,
          "naive_asset_volatility": 0.897801987768,
          "naive_distance_to_default": 0.843622285632,
          "naive_default_probability": 0.199440253471,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 60,
        "value": 0.827425527032,
        "value_label": "0.8274 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.8274 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 60.0,
          "equity_volatility": 1.2,
          "prior_year_equity_return": 0.08,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 180.0,
          "naive_debt_volatility": 0.35,
          "naive_asset_volatility": 0.916666666667,
          "naive_distance_to_default": 0.827425527032,
          "naive_default_probability": 0.203997958454,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      }
    ]
  },
  {
    "name": "Failure/comparison",
    "description": "Synthetic failure/comparison sweep; only declared fields change while the topic contract remains fixed.",
    "canonical_step": 30,
    "summary": {
      "focus_step": 30,
      "focus_kind": "comparison",
      "canonical_output_match": false,
      "state_counts": {
        "calculated": 61
      },
      "value_min": -0.062595511164,
      "value_max": 4.957790867642,
      "segments": [
        {
          "start_step": 0,
          "end_step": 60,
          "state": "calculated",
          "decision": "bharath-shumway-naive-approximation",
          "start_value_label": "-0.0626 sigma",
          "end_value_label": "4.9578 sigma"
        }
      ]
    },
    "states": [
      {
        "step": 0,
        "value": -0.062595511164,
        "value_label": "-0.0626 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting -0.0626 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 180.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.5,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 300.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.2225,
          "naive_distance_to_default": -0.062595511164,
          "naive_default_probability": 0.524955698009,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 1,
        "value": 0.025284028696,
        "value_label": "0.0253 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.0253 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 178.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.483333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 298.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.222879464286,
          "naive_distance_to_default": 0.025284028696,
          "naive_default_probability": 0.489914206557,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 2,
        "value": 0.113019253875,
        "value_label": "0.1130 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.1130 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 177.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.466666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 297.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.223262331839,
          "naive_distance_to_default": 0.113019253875,
          "naive_default_probability": 0.455007645315,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 3,
        "value": 0.20060975345,
        "value_label": "0.2006 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.2006 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 176.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.45,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 296.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.223648648649,
          "naive_distance_to_default": 0.20060975345,
          "naive_default_probability": 0.420501865482,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 4,
        "value": 0.288055133105,
        "value_label": "0.2881 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.2881 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 174.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.433333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 294.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.224038461538,
          "naive_distance_to_default": 0.288055133105,
          "naive_default_probability": 0.386652268092,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 5,
        "value": 0.375355016086,
        "value_label": "0.3754 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.3754 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 173.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.416666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 293.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.224431818182,
          "naive_distance_to_default": 0.375355016086,
          "naive_default_probability": 0.353698227577,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 6,
        "value": 0.462509044204,
        "value_label": "0.4625 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.4625 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 172.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.4,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 292.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.224828767123,
          "naive_distance_to_default": 0.462509044204,
          "naive_default_probability": 0.321858159034,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 7,
        "value": 0.549516878878,
        "value_label": "0.5495 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.5495 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 170.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.383333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 290.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.225229357798,
          "naive_distance_to_default": 0.549516878878,
          "naive_default_probability": 0.291325392216,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 8,
        "value": 0.636378202243,
        "value_label": "0.6364 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.6364 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 169.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.366666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 289.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.225633640553,
          "naive_distance_to_default": 0.636378202243,
          "naive_default_probability": 0.262264972421,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 9,
        "value": 0.723092718295,
        "value_label": "0.7231 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.7231 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 168.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.35,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 288.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.226041666667,
          "naive_distance_to_default": 0.723092718295,
          "naive_default_probability": 0.234811461327,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 10,
        "value": 0.80966015411,
        "value_label": "0.8097 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.8097 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 166.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.333333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 286.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.226453488372,
          "naive_distance_to_default": 0.80966015411,
          "naive_default_probability": 0.209067762451,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 11,
        "value": 0.896080261107,
        "value_label": "0.8961 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.8961 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 165.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.316666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 285.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.226869158879,
          "naive_distance_to_default": 0.896080261107,
          "naive_default_probability": 0.185104949239,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 12,
        "value": 0.982352816385,
        "value_label": "0.9824 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 0.9824 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 164.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.3,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 284.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.227288732394,
          "naive_distance_to_default": 0.982352816385,
          "naive_default_probability": 0.162963031409,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 13,
        "value": 1.06847762412,
        "value_label": "1.0685 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.0685 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 162.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.283333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 282.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.227712264151,
          "naive_distance_to_default": 1.06847762412,
          "naive_default_probability": 0.142652559251,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 14,
        "value": 1.154454517033,
        "value_label": "1.1545 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.1545 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 161.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.266666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 281.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.228139810427,
          "naive_distance_to_default": 1.154454517033,
          "naive_default_probability": 0.124156937679,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 15,
        "value": 1.240283357932,
        "value_label": "1.2403 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.2403 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 160.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.25,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 280.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.228571428571,
          "naive_distance_to_default": 1.240283357932,
          "naive_default_probability": 0.107435302835,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 16,
        "value": 1.325964041333,
        "value_label": "1.3260 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.3260 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 158.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.233333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 278.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.229007177033,
          "naive_distance_to_default": 1.325964041333,
          "naive_default_probability": 0.092425804204,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 17,
        "value": 1.411496495159,
        "value_label": "1.4115 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.4115 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 157.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.216666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 277.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.229447115385,
          "naive_distance_to_default": 1.411496495159,
          "naive_default_probability": 0.079049134164,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 18,
        "value": 1.496880682532,
        "value_label": "1.4969 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.4969 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 156.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.2,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 276.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.229891304348,
          "naive_distance_to_default": 1.496880682532,
          "naive_default_probability": 0.067212153754,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 19,
        "value": 1.582116603643,
        "value_label": "1.5821 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.5821 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 154.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.183333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 274.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.230339805825,
          "naive_distance_to_default": 1.582116603643,
          "naive_default_probability": 0.056811476946,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 20,
        "value": 1.667204297739,
        "value_label": "1.6672 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.6672 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 153.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.166666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 273.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.230792682927,
          "naive_distance_to_default": 1.667204297739,
          "naive_default_probability": 0.047736894229,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 21,
        "value": 1.752143845188,
        "value_label": "1.7521 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.7521 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 152.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.15,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 272.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.23125,
          "naive_distance_to_default": 1.752143845188,
          "naive_default_probability": 0.039874538326,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 22,
        "value": 1.836935369674,
        "value_label": "1.8369 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.8369 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 150.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.133333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 270.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.23171182266,
          "naive_distance_to_default": 1.836935369674,
          "naive_default_probability": 0.033109718523,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 23,
        "value": 1.921579040487,
        "value_label": "1.9216 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 1.9216 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 149.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.116666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 269.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.232178217822,
          "naive_distance_to_default": 1.921579040487,
          "naive_default_probability": 0.027329373999,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 24,
        "value": 2.006075074949,
        "value_label": "2.0061 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.0061 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 148.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.1,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 268.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.232649253731,
          "naive_distance_to_default": 2.006075074949,
          "naive_default_probability": 0.022424119353,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 25,
        "value": 2.090423740954,
        "value_label": "2.0904 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.0904 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 146.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.083333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 266.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.233125,
          "naive_distance_to_default": 2.090423740954,
          "naive_default_probability": 0.018289876049,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 26,
        "value": 2.174625359653,
        "value_label": "2.1746 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.1746 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 145.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.066666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 265.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.233605527638,
          "naive_distance_to_default": 2.174625359653,
          "naive_default_probability": 0.014829101176,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 27,
        "value": 2.258680308279,
        "value_label": "2.2587 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.2587 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 144.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.05,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 264.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.234090909091,
          "naive_distance_to_default": 2.258680308279,
          "naive_default_probability": 0.011951639122,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 28,
        "value": 2.342589023121,
        "value_label": "2.3426 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.3426 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 142.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.033333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 262.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.234581218274,
          "naive_distance_to_default": 2.342589023121,
          "naive_default_probability": 0.009575232369,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 29,
        "value": 2.42635200266,
        "value_label": "2.4264 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.4264 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 141.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": -0.016666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 261.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.235076530612,
          "naive_distance_to_default": 2.42635200266,
          "naive_default_probability": 0.007625734731,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 30,
        "value": 2.50996981088,
        "value_label": "2.5100 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5100 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 140.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.0,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 260.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.235576923077,
          "naive_distance_to_default": 2.50996981088,
          "naive_default_probability": 0.006037074173,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 31,
        "value": 2.593443080751,
        "value_label": "2.5934 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.5934 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 138.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.016666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 258.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.236082474227,
          "naive_distance_to_default": 2.593443080751,
          "naive_default_probability": 0.00475101331,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 32,
        "value": 2.676772517915,
        "value_label": "2.6768 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.6768 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 137.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.033333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 257.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.236593264249,
          "naive_distance_to_default": 2.676772517915,
          "naive_default_probability": 0.003716754305,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 33,
        "value": 2.759958904565,
        "value_label": "2.7600 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.7600 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 136.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.05,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 256.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.237109375,
          "naive_distance_to_default": 2.759958904565,
          "naive_default_probability": 0.002890431646,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 34,
        "value": 2.843003103551,
        "value_label": "2.8430 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.8430 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 134.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.066666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 254.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.237630890052,
          "naive_distance_to_default": 2.843003103551,
          "naive_default_probability": 0.002234531762,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 35,
        "value": 2.925906062711,
        "value_label": "2.9259 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 2.9259 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 133.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.083333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 253.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.238157894737,
          "naive_distance_to_default": 2.925906062711,
          "naive_default_probability": 0.001717273136,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 36,
        "value": 3.008668819446,
        "value_label": "3.0087 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.0087 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 132.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.1,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 252.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.23869047619,
          "naive_distance_to_default": 3.008668819446,
          "naive_default_probability": 0.001311974877,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 37,
        "value": 3.091292505564,
        "value_label": "3.0913 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.0913 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 130.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.116666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 250.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.239228723404,
          "naive_distance_to_default": 3.091292505564,
          "naive_default_probability": 0.000996436055,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 38,
        "value": 3.173778352394,
        "value_label": "3.1738 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.1738 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 129.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.133333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 249.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.239772727273,
          "naive_distance_to_default": 3.173778352394,
          "naive_default_probability": 0.000752342735,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 39,
        "value": 3.256127696202,
        "value_label": "3.2561 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.2561 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 128.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.15,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 248.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.240322580645,
          "naive_distance_to_default": 3.256127696202,
          "naive_default_probability": 0.000564714717,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 40,
        "value": 3.338341983921,
        "value_label": "3.3383 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.3383 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 126.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.166666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 246.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.240878378378,
          "naive_distance_to_default": 3.338341983921,
          "naive_default_probability": 0.000421399755,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 41,
        "value": 3.420422779221,
        "value_label": "3.4204 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.4204 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 125.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.183333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 245.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.241440217391,
          "naive_distance_to_default": 3.420422779221,
          "naive_default_probability": 0.000312619418,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 42,
        "value": 3.502371768937,
        "value_label": "3.5024 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.5024 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 124.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.2,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 244.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.242008196721,
          "naive_distance_to_default": 3.502371768937,
          "naive_default_probability": 0.000230567846,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 43,
        "value": 3.584190769881,
        "value_label": "3.5842 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.5842 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 122.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.216666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 242.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.242582417582,
          "naive_distance_to_default": 3.584190769881,
          "naive_default_probability": 0.000169062446,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 44,
        "value": 3.665881736073,
        "value_label": "3.6659 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.6659 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 121.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.233333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 241.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.243162983425,
          "naive_distance_to_default": 3.665881736073,
          "naive_default_probability": 0.000123243912,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 45,
        "value": 3.7474467664,
        "value_label": "3.7474 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.7474 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 120.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.25,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 240.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.24375,
          "naive_distance_to_default": 3.7474467664,
          "naive_default_probability": 8.9321867e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 46,
        "value": 3.82888811276,
        "value_label": "3.8289 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.8289 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 118.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.266666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 238.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.244343575419,
          "naive_distance_to_default": 3.82888811276,
          "naive_default_probability": 6.4361754e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 47,
        "value": 3.9102081887,
        "value_label": "3.9102 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.9102 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 117.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.283333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 237.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.244943820225,
          "naive_distance_to_default": 3.9102081887,
          "naive_default_probability": 4.6108303e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 48,
        "value": 3.9914095786,
        "value_label": "3.9914 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 3.9914 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 116.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.3,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 236.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.245550847458,
          "naive_distance_to_default": 3.9914095786,
          "naive_default_probability": 3.2840866e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 49,
        "value": 4.072495047437,
        "value_label": "4.0725 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.0725 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 114.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.316666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 234.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.246164772727,
          "naive_distance_to_default": 4.072495047437,
          "naive_default_probability": 2.3256095e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 50,
        "value": 4.153467551173,
        "value_label": "4.1535 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.1535 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 113.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.333333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 233.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.246785714286,
          "naive_distance_to_default": 4.153467551173,
          "naive_default_probability": 1.6373733e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 51,
        "value": 4.234330247806,
        "value_label": "4.2343 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.2343 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 112.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.35,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 232.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.247413793103,
          "naive_distance_to_default": 4.234330247806,
          "naive_default_probability": 1.1461693e-05,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 52,
        "value": 4.315086509148,
        "value_label": "4.3151 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.3151 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 110.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.366666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 230.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.248049132948,
          "naive_distance_to_default": 4.315086509148,
          "naive_default_probability": 7.977021e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 53,
        "value": 4.395739933375,
        "value_label": "4.3957 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.3957 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 109.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.383333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 229.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.248691860465,
          "naive_distance_to_default": 4.395739933375,
          "naive_default_probability": 5.519802e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 54,
        "value": 4.476294358403,
        "value_label": "4.4763 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.4763 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 108.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.4,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 228.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.249342105263,
          "naive_distance_to_default": 4.476294358403,
          "naive_default_probability": 3.797488e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 55,
        "value": 4.556753876172,
        "value_label": "4.5568 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.5568 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 106.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.416666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 226.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.25,
          "naive_distance_to_default": 4.556753876172,
          "naive_default_probability": 2.597512e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 56,
        "value": 4.637122847893,
        "value_label": "4.6371 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.6371 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 105.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.433333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 225.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.250665680473,
          "naive_distance_to_default": 4.637122847893,
          "naive_default_probability": 1.766462e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 57,
        "value": 4.717405920338,
        "value_label": "4.7174 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.7174 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 104.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.45,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 224.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.251339285714,
          "naive_distance_to_default": 4.717405920338,
          "naive_default_probability": 1.194354e-06,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 58,
        "value": 4.79760804326,
        "value_label": "4.7976 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.7976 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 102.666666666667,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.466666666667,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 222.666666666667,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.252020958084,
          "naive_distance_to_default": 4.79760804326,
          "naive_default_probability": 8.02858e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 59,
        "value": 4.877734488039,
        "value_label": "4.8777 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.8777 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 101.333333333333,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.483333333333,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 221.333333333333,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.252710843373,
          "naive_distance_to_default": 4.877734488039,
          "naive_default_probability": 5.36556e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      },
      {
        "step": 60,
        "value": 4.957790867642,
        "value_label": "4.9578 sigma",
        "state": "calculated",
        "diagnostic": "calculated: bharath-shumway-naive-approximation",
        "guidance": "Inspect the intermediate components before interpreting 4.9578 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "debt_face_value": 100.0,
          "equity_volatility": 0.35,
          "prior_year_equity_return": 0.5,
          "horizon_years": 1.0
        },
        "output": {
          "naive_firm_value": 220.0,
          "naive_debt_volatility": 0.1375,
          "naive_asset_volatility": 0.253409090909,
          "naive_distance_to_default": 4.957790867642,
          "naive_default_probability": 3.56496e-07,
          "state": "calculated",
          "reason": "bharath-shumway-naive-approximation"
        }
      }
    ]
  }
]